G. H. Hardy: Quotes about ideas and thoughts

G. H. Hardy was British mathematician. Explore interesting quotes on idea.
G. H. Hardy: 40   quotes 23   likes

“Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. …There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts.
The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. …Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers.”

G. H. Hardy

"The Theory of Numbers," Nature (Sep 16, 1922) Vol. 110 https://books.google.com/books?id=1bMzAQAAMAAJ p. 381

Beauty , Mountain , Mathematics , Idea

“The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

World , Beauty , Way , Mathematics

“A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, […] the importance of ideas in poetry is habitually exaggerated: '… Poetry is not the thing said but a way of saying it.' [In poetry, ] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

Beauty , Way , Idea , Painting

“Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

Mathematics , Idea , Chance

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

Idea